A falsehood is a lie. If your mom has an uncanny knack for knowing when you're telling a falsehood, it means she always knows when you're stretching the truth.
The noun falsehood is a slightly fancy or old-fashioned way of saying "lie." It's hard to ever completely trust a friend again once he's told you a falsehood, although sometimes people tell small falsehoods simply to make others feel better. Telling your aunt her pink hair looks fine is a small falsehood, while lying about your grades on a college application is a pretty big falsehood. The Latin root is falsus, "deceived or erroneous."